scholarly journals Predicting crystal structures and properties of matter under extreme conditions via quantum mechanics: the pressure is on

2015 ◽  
Vol 17 (5) ◽  
pp. 2917-2934 ◽  
Author(s):  
Eva Zurek ◽  
Wojciech Grochala
Keyword(s):  
Quantum Mechanics ◽  
Crystal Structures ◽  
Quantum Mechanical ◽  
Extreme Conditions ◽  
Quantum Mechanical Calculations ◽  
Structures And Properties

The role of quantum mechanical calculations in understanding and predicting the behavior of matter at extreme pressures is discussed in this feature contribution.

On the error of approximations in quantum mechanics. I. General theory

1965 ◽  
Vol 257 (1081) ◽  
pp. 309-326 ◽  
Keyword(s):  
Quantum Mechanics ◽  
General Theory ◽  
Computer Applications ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
Density Matrices ◽  
Single Error

General formulas for estimating the errors in quantum-mechanical calculations are given in the formalism of density matrices. Some properties of the traces of matrices are used to simplify the estimating and to indicate a way of obtaining a better approximation. It is shown that the simultaneous correction of all the equations to be fulfilled leads in most cases to a faster convergence than the exact fulfilment of some of the equations and approximating stepwise to some of the others. The corrective formulas contain only direct operations of the matrices occurring and so they are advantageous in computer applications. In the last section a ‘subjective error’ definition is given and by taking into account the weight of the errors of the several equations a faster convergence and a single error quantity is obtained. Some special applications of the method will be published later.

scholarly journals Детерминизм локального атомного упорядочения в монослоях золота в формировании их электронной структуры

2022 ◽  
Vol 64 (3) ◽  
pp. 303
Author(s):  
В.Л. Карбовский ◽  
А.А. Романский ◽  
Л.И. Карбовская ◽  
В.В. Стонис
Keyword(s):  
Coordination Sphere ◽  
Electronic States ◽  
Mutual Arrangement ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
The Third ◽  
Long Range Interactions ◽  
Valence Bands ◽  
D Orbitals

The total and partial densities of electronic states of gold monolayer structures of different symmetry are calculated by the quantum mechanical calculations methods in the DFT approximation. It is shown that the first coordination sphere is determinant in the formation of the fine structure and the extent of the valence bands of the monolayer gold structures under study. The peaks splitting of the TDOS curve, which leads to its finer structure, is influenced not only by the lengths of interatomic bonds but also by the mutual arrangement of atoms. The influence of long-range interactions on the electronic structure of gold monolayers has been established. For example, for the (110) plane, a change in the atomic ordering in the third coordination sphere as a result of the introduction of a vacancy leads to noticeable changes in the TDOS curve, which indicates either a significant role of the atoms of the third coordination sphere or a significant redistribution of the interaction of d-orbitals of different symmetries of close neighbours. A correlation between the packing density, as well as the number of neighbours in the first coordination sphere, and the width of the energy band of gold monolayers has been established.

scholarly journals THE SCHWINGER REPRESENTATION OF A GROUP: CONCEPT AND APPLICATIONS

2006 ◽  
Vol 18 (08) ◽  
pp. 887-912 ◽  
Author(s):  
S. CHATURVEDI ◽  
G. MARMO ◽  
N. MUKUNDA ◽  
R. SIMON ◽  
A. ZAMPINI
Keyword(s):  
Quantum Mechanics ◽  
Lie Group ◽  
Irreducible Representations ◽  
Quantum Mechanical ◽  
Direct Sum ◽  
Pure States ◽  
Group Concept ◽  
Set Up ◽  
Multiplicity Free

The concept of the Schwinger Representation of a finite or compact simple Lie group is set up as a multiplicity-free direct sum of all the unitary irreducible representations of the group. This is abstracted from the properties of the Schwinger oscillator construction for SU(2), and its relevance in several quantum mechanical contexts is highlighted. The Schwinger representations for SU(2), SO(3) and SU(n) for all n are constructed via specific carrier spaces and group actions. In the SU(2) case, connections to the oscillator construction and to Majorana's theorem on pure states for any spin are worked out. The role of the Schwinger Representation in setting up the Wigner–Weyl isomorphism for quantum mechanics on a compact simple Lie group is brought out.

Significance of hydrogen bonding networks in the proton-coupled electron transfer reactions of photosystem II from a quantum-mechanics perspective

2019 ◽  
Vol 21 (17) ◽  
pp. 8721-8728 ◽  
Author(s):  
Jun Chai ◽  
Zhaoyang Zheng ◽  
Hui Pan ◽  
Shengbai Zhang ◽  
K. V. Lakshmi ◽  
...  
Keyword(s):  
Electron Transfer ◽  
Hydrogen Bonding ◽  
Quantum Mechanics ◽  
Photosystem Ii ◽  
Transfer Reactions ◽  
Quantum Mechanical ◽  
Quantum Mechanical Calculations ◽  
Electron Transfer Reactions ◽  
Proton Coupled Electron Transfer ◽  
Hydrogen Bonding Networks

All quantum-mechanical calculations provide insights into the effect of the hydrogen bonding network on the proton-coupled electron transfer at YZ and YD in photosystem II.

Sign in / Sign up

Export Citation Format

Share Document